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Unit-3

FUNDAMENTALS OF ROCKET PROPULSION

Operating principle Specific impulse of a rocket internal ballistics- Rocket nozzle

classification Rocket performance considerations Numerical Problems.

Rockets Special Features and Applications

Historical Reference The basic principles of all propulsive devices lie with the laws of motion due to Newton

(17th

Century AD). These laws are phenomenological and therefore one can expect that

even before Newton there may have existed many devices working on the principles of

reaction.

Rockets working directly on the principle of reaction are perhaps the simplest of thepropulsive engines.

The reciprocating engines and gas turbine engines are relatively more complex. The Chinese are credited with the invention of rockets probably in 12-14th century AD. Indians used the rockets as effective weapons in late 18 th century against British and in

19th century, the rockets became a part of the warfare in Europe. But it was only in the

early part of the present century that man has recognized the full potential of rocket

owing to the interests in space travel/satellite technology and like.

Tsiolkovsky (USSR 1903) Goddard (USA, 1912) and Oberth (1921) are the pioneers ofmodern rocketry.

The liquid propellant rocket owe their genesis to these people. The German V-2 rockets (25 tons, 65 sec, LOX-Alchol) and the post-second World war

progress in rocketry are too familiar to all.

Principle

All the conventional propulsion systems work by causing a change of momentum in a working

fluid in a direction opposite to the intended motion. Rockets fall under the category of direct

acting engines since the energy liberated by the chemical process is directly used to obtain

thrust. Being non-air breathing devices the basic component of a rocket are

(i) Combustion chamber where exothermic processes produces gases at high temperatureand pressure, and

(ii)Nozzle, which accelerate the fluid to high velocities and discharge them into surroundingatmosphere thereby deriving the desired force or thrust.

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Some Special Features

The non-air breathing nature of rockets makes them very distinct among the propulsive devices.

(a)The reaction system does not depend on the surrounding atmosphere. There are novelocity limitations and altitude ceiling.

(b)Since it has to carry its own oxidizer required for combustion reaction, the specificpropellant consumption is very high. Rockets consume approximately 15kg/kg-hr of

propellant compared to about 1 kg/kg-hr of fuel by turbojet engine.

(c)High pressure operation is possible and hence the ratio of energy liberation per unitvolume (and also unit weight of hardware) is very high.

(d)Main part of the rockets contains no moving element. Hence there is no constraint oninternal aerodynamics and the reliability is high. This also implies quick response times,

which makes them ideal control components.

With the above features, it is clear that the rockets are the most suitable power plants for

(i)

High altitude and space applications where atmospheric oxygen is not available,eg. Launch vehicles and satellite control rockets.

(ii) All applications where high thrust are required for short duration: missiles, boosters,JATO etc.

Rockets in Space Applications

There are a variety of rockets when it comes to launching and satellite control. Many of these are

non-chemical in nature but are restricted to extremely low thrust levels.

Sl

No Type

Order of

Magnitude ofThrust (N) F/W OperationalTime

Isp

(sec) Applications

1

Solar sail

(not a rocket in

fact)

10-5

10-4

Years Satellite Altitude

control

2

Electric Prop.

(Electro thermal,

Electro Static,

Electro

Magnetic)

10-6 - 10-2 10-5-10-3 Years 150 - 6000

Satellite control,

stabilization, orbit

maneuver

3Stored cold gas

(N2, NH3 etc.)10-2 - 10-1 ~ 10-3 Years 50 - 100 -do-

4 Nuclear Rocket upto 105 20-30 Minute tohours 800 Interplanetary andspace travel

5

Chemical Rocket

(Solid, Liquid

and Hybrid)

upto 107 upto 80Seconds to

minutes@150-450

Launch vehicles,

Missiles, Control

rockets, Sounding

rockets, JATO etc

@ shuttle main engine operate for about 8 min at a time but over 7 hrs cumulatively.

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Classification of Chemical Rockets

Depending on the context, the chemical rockets are classified in many ways as follows:

(a)Type of propellant: Solid, Liquid (mono propellant / bipropellant and hybrid rockets)(b)Application: Launch vehicle, ABMs, JATOs, ICBM, IRBM, SAM etc.(c)Size of Unit (and thrust level sometimes): 10 ton, 100 kg etc.(d)Type of subsystem: Turbopump fed, clustering, grain type etc.

Specific Impulse

The specific impulse of a rocket,Isp, is the ratio of the thrust to the flow rate of the weight ejected,that is

where Fis thrust, is the rate of mass flow, and g is the acceleration of gravity at ground

level.

Specific impulse is expressed in seconds. When the thrust and the flow rate remain constantthroughout the burning of the propellant, the specific impulse is the time for which the rocket

engine provides a thrust equal to the weight of the propellant consumed.

For a given engine, the specific impulse has different values on the ground and in the vacuum ofspace because the ambient pressure is involved in the expression for the thrust. It is therefore

important to state whether specific impulse is the value at sea level or in a vacuum.

There are a number of losses within a rocket engine, the main ones being related to theinefficiency of the chemical reaction (combustion) process, losses due to the nozzle, and losses

due to the pumps.

Overall, the losses affect the efficiency of the specific impulse. This is the ratio of the realspecific impulse (at sea level, or in a vacuum) and the theoretical specific impulse obtained with

an ideal nozzle from gases coming from a complete chemical reaction. Calculated values of

specific impulse are several percent higher than those attained in practice.

From Equation (2.8) we can substitute C for Fin Equation (2.23), thus obtaining

Equation (2.24) is very useful when solving Equations (2.18) through (2.21). It is rare we aregiven the value ofCdirectly, however rocket engine specific impulse is a commonly given

parameter.

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Internal Ballistics

The parameters that govern the burning rate and mass discharge rate of rocket motors are called

internal ballistic properties; they include

r propellant burning rate (velocity of consumption), m/sec or mm/sec or in/sec.

K ratio of burning surface to throat area, Ab/At

p temperature sensitivity of burning rate, expressed as percent change of burning

rate per degree change in propellant temperature at a particular value of chamber

pressure.

K - temperature sensitivity of pressure expressed as percent change of chamber

pressure per degree change in propellant temperature at a particular value of K,

and the influences caused by pressure, propellant ingredients, gas velocity, or acceleration.

The subsequent solid propellant rocket parameters are performance parameters; they include

thrust, ideal exhaust velocity, specific impulse, propellant mass fraction, flame temperature,

temperature limits and duration.

Propellant Burning Rate

The rocket motors operation and design depend on the combustion characteristics of the

propellant, its burning rate, burning surface, and grain geometry. The branch of applied science

describing these is known as internal ballistics.

Solid propellant burns normal to its surface. The (average) burning rate, r, is defined as theregression of the burning surface per unit time. For a given propellant, the burning rate is mainly

dependent on the pressure, p, and the initial temperature, Ti, of the propellant. Burning rate is

also a function of propellant composition. For composite propellants it can be increased by

changing the propellant characteristics:

1. Add a burning rate catalyst, often called burning rate modifier (0.1 to 3.0% of propellant)or increase percentage of existing catalyst.

2. Decrease the oxidizer particle size.3. Increase oxidizer percentage4. Increase the heat of combustion of the binder and/or the plasticizer5. Imbed wires or metal staples in the propellant

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Apart from the propellant formulation and propellant manufacturing process, burning ratein a

full-scale motor can be increased by the following

1. Combustion chamber pressure2. Initial temperature of the solid propellant prior to start3. Combustion gas temperature4. Velocity of the gas flow parallel to the burning surface5. Motor motion ( acceleration and spin-induced grain stress)

Burning rate data are usually obtained in three ways namely, from testing by:

1. Standard strand burners, often called Crawford burners2. Small-scale ballistic evaluation motors3. Full-scale motors with good instrumentation

A strand burner is a small pressure vessal (usually with windows) in which a thin strand

or bar of propellant is ignited at one end and burned to the other end. The strand can be

inhibited with an external coating so that it will burn only on the exposed cross-sectionalsurface; chamber pressure is simulated by pressurizing the container with inert gas. The

burning rate can be measured by electric signals from embedded wires, by ultrasonic

waves, or by optical means. The burning rate measured on strand burners is usually lower

than that obtained from actual rocket motor firing (by 4 to 12%) because it does not truly

simulate the hot chamber environment of an actual rocket motor. Also small ballistic

evaluation motors usually have a slightly lower burning rate than full-scale large motors,

because of scaling factors.

During development of a new or modified solid propellant, it is tested extensively or

characterized. This includes the testing of the burn rate (in several different ways) underdifferent temperatures, pressures, impurities, and conditions. It also requires

measurements of physical, chemical, and manufacturing properties, ignitability, aging,

sensitivity to various energy inputs or stimuli (e.g., shock, friction, fires), moister

absorption, compatibility with other materials (liners, insulators, cases), and other

characteristics. It is a lengthy, expensive, often hazardous program with many tests,

samples, and analyses.

The burning rate of propellant in a motor is a function of many parameters, and at any

instant governs the mass flow rate m

of hot gas generated and flowing from the motor(stable combustion);

m

= Ab r b

Here Ab is the burning area of the propellant grain, r the burning rate, and b the solid

propellant density prior to motor start. The total mass m of effective propellant burned can be

determined by integrating the above equation,

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dtrAdtmm bb ==

Where Ab and r vary with time and pressure.

Burning Rate Relation with Pressure

Classical equations relating to burning rate are helpful in preliminary design, data extrapolation,

and understanding the phenomena. Unless otherwise stated, burning rate is expressed for 70oF or

294 K propellant (prior to ignition) burning at a reference chamber pressure of 1000 psia or

6.895 MPa. For most production-type propellant the burning rate is approximated as a function

of chamber pressure, at least for a limited range of chamber pressures, which is given as

r = aPn

where r, the burn rate, is usually in centimeter per second and chamber pressure P is in MPa; a is

an empirical constant influenced by ambient temperature. Also a is known as the temperature

coefficient and it is NOT dimensionless. The burning rate exponent n, sometimes called the

combustion index, is independent of the initial grain temperature and describes the influence ofchamber pressure on the burning rate.

Burning Rate Relation with Temperature

Temperature affects chemical reaction rates and the initial ambient temperature of a propellant

grain prior to combustion influences burning rate.

The sensitivity of burning rate to propellant temperature can be expressed in the form of

temperature coefficient, the two most common being

KK

K

pp

p

T

P

PT

p

Tr

rTr

=

=

=

=

1ln

1ln

with p , temperature sensitivity of burning rate and K, temperature sensitivity of pressure.

The coefficient p (typically 0.001 0.009 / K) for a new propellant is usually calculated from

strand burner test data, andK (typically 0.067 0.278 % /oC) from small-scale or full-scale

motors. Mathematically, these coefficients are the partial derivatives of the natural logarithm ofthe burning rate r or the chamber pressure p, respectively, with respect to propellant temperature

T.

The values of K and p depend primarily on the nature of the propellant burning rate, the

composition, and the combustion mechanism of the propellant. It is possible to derive a

relationship between the two temperature sensitivities, namely

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pKn

=

1

1

This formula is usually valid when the three variables are constant over the chamber pressure

and temperature range.

The temperature sensitivity p can be also expressed as

dT

da

aT

aP

p

n

p

1)(ln=

=

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Equilibrium chamber pressure

In the above figure the straight line through the origin and point S depicts the mass flow

through the nozzle as a function of Pc. At point S there is a balance between mass production and

outflux of the mass. At higher pressures (>__

cP ) the mass flow through the nozzle is larger than

the production at the burning surface in case n < 1 and the reverse happens for n > 1. Thus if

n < 1 the pressure will drop to its steady-state value__

cP . Note that when n < 1 even at higher

chamber pressure rocket motor will back to its designed equilibrium chamber pressure and

ensure a stable operation. On the other hand when n>1 these types of situations will possibly lead

to over-pressurization and rupture of the rocket motor or depressurization and flame out.

Erosive Burning

Erosive burning refers to the increase in the propellant burning caused by the high-velocity flow

of combustion gases over the burning propellant surface. It can seriously affect the performance

of solid propellant rocket motors. It occurs primarily in the port passages or perforations of the

grain as the combustion gases flow toward the nozzle; it is more likely to occur ehen the port

passage cross-sectional area A is small relative to the throat area At with a port-to-throat area

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ratio of 4 or less. The high velocity near the burning surface and the turbulent mixing in the

boundary layers increase the heat transfer to the solid propellant and thus increase the burning

rate.

Erosive burning increases the mass flow and thus also the chamber pressure and thrust during

the early portion of the burning for a particular motor (see above Fig.). Erosive burning causes

early burnout of the web, usually at the nozzle end, and exposes the insulation and aft closure to

hot combustion gas for a longer period of time; this usually requires more insulation layer

thickness (and more inert mass) to prevent local thermal failure. In designing motors, erosive

burning is either avoided or controlled to be reproducible from one motor to the next.

Total burning rate = steady state burning rate (n

caP ) + erosive burning

Basic Performance Relations

One basic performance relation derived from the principle of conservation of matter. The

propellant mass burned per unit time has to equal the sum of the change in gas mass per unit time

in the combustion chamber grain cavity and the mass flowing out through the exhaust nozzle per

unit time.

)1/()1(

1

1111

2)(

+

++=

kk

tbbkRT

kPAV

dt

drA

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The term on the left side of the equation gives the mass rate of gas generation. The first term on

the right gives the change in propellant mass in the gas volume of the combustion chamber, and

the last term gives the nozzle flow. The burning rate of propellant is r; Ab is the propellant

burning area; b is the solid propellant density; 1 is the combustion gas density; V1 is the

chamber gas cavity volume, which becomes larger as the propellant is expended; At is the throat

area; P1 is the chamber pressure; T1 is the absolute chamber temperature, which is usually

assumed to be constant; and k is the specific heat ratio of the combustion gases. During startup

the changing mass of propellant in the grain cavity becomes important.

Isentropic Flow through Nozzles

In a converging diverging nozzle a large fraction of the thermal energy of the gases in the

chamber is converted into kinetic energy. As will be explained, the gas pressure and temperature

drop dramatically and gas velocity can reach values in excess of around 3.2 km/sec. This is a

reversible, essentially isentropic flow process.

If a nozzle inner wall has a flow obstruction or a wall protrusion (a piece of weld splatter or

slag), then the kinetic gas energy is locally converted back into thermal energy essentially equal

to the stagnation temperature and stagnation pressure in the chamber. Since this would lead

quickly to a local overheating and failure of the wall, nozzle inner walls have to be smooth

without any protrusion.

Nozzle exit velocity can be derived as,

2

1

/)1(

1

212 1

1

2v

P

PRT

k

kv

kk

+

=

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This relation also holds for any two points within the nozzle. Note that when the chamber section

is large compared to the nozzle throat section, the chamber velocity or nozzle approach velocity

is comparatively small and the 21v can be neglected. The chamber temperature T1 is at the nozzle

inlet and, under isentropic condition, differ little from the stagnation temperature or (for a

chemical rocket) from combustion temperature. This leads to an important simplified expressionof the exhaust velocity v2, which is often used in the analysis.

=

kk

P

PRT

k

kv

/)1(

1

212 1

1

2

=

kk

o

P

P

M

TR

k

k/)1(

1

2

'

11

2

Thrust and Thrust Coefficient

2322 )( AppvmF +=

1PACF tF=

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Where CF is the thrust coefficient, which can be derived as a function of gas property k, the

nozzle area ratio (A2/At), and the pressure ratio across the nozzle p1/p2 , but independent of

chamber temperature. For any fixed pressure ratio (p1/p3) the thrust coefficient CF and the thrust

F have a peak when p2 = p3. This peak value is known as optimum thrust coefficient.

t

kkkk

FA

A

p

pp

p

p

kk

kC 2

1

32

/)1(

1

2

)1/()1(2

11

2

1

2 +

+=

+

Effective Exhaust Velocity

In a rocket nozzle the actual exhaust velocity is not uniform over the entire exit cross-section and

does not represent the entire thrust magnitude. The velocity profile is difficult to measure

accurately. For convenience a uniform axial velocity c is assumed which allows a one-

dimensional description of the problem. This effective exhaust velocity c is the averageequivalent velocity at which propellant is ejected from the vehicle. It is defined as

==

m

FgIc osp

It is usually given in meters per second.

The concept of weight relates to the gravitational attraction at or near sea level, but in space or

outer satellite orbits, weight signifies the mass multiplied by an arbitrary constant, namely g o.

In system international (SI) or metric system of units Isp

can be expressed simply in seconds,

because of the use of the constant go.

Specific Propellant Consumption

Specific propellant consumption is the reciprocal of the specific impulse.

Mass Ratio

The mass ratio of a vehicle or a particular vehicle stage is defined to be the final mass m f(after

rocket operation has consumed all usable propellant) divided by initial mass mo (before rocket

operation).

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This applies to a single or multi-stage vehicle. The final mass mfis the mass of the vehicle after

the rocket has ceased to operate when all the useful propellant mass mp has been consumed and

ejected. The final vehicle mass mf includes all those components that are not useful propellant

and may include guidance devices, navigation gear, payload (e.g., scientific instruments or a

military warhead), flight control systems, communication devices, power supplies, tank

structure, residual or unusable propellant, and all the propulsion hardware. In some vehicles it

can also include wings, fins, a crew, life support systems, reentry shields, landing gears etc.

Typical value of Mass ratio can range from 60% for tactical missiles to less than 10 % for

unmanned launch vehicle stages. This mass ratio is an important parameter in analyzing flight

performance. Note that when mass-ratio is applied to a single stage of a multi-stage rocket, then

its upper stages become the payload

Propellant Mass Fraction,

Propellant mass fraction is defined as the ratio of propellant mass mpto the initial mass mo

o

p

m

m=

mo = mf + mp

Characteristic Velocity

The characteristic velocity has been used frequently in the rocket propulsion literature. It is

represented by a symbol C

*

. It is defined as,

=

m

ApC t1

The characteristic velocity is used in comparing the relative performance of different chemical

rocket propulsion system designs and propellants. It is basically a function of the propellant

characteristics. It is easily determined from data of

m , p1, and At. It relates to the efficiency of

the combustion and is essentially independent of nozzle characteristics. However, the specific

impulse and the effective exhaust velocities are functions of the nozzle geometry, such as the

nozzle area ratio.

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Problems:

Q1.

A rocket projectile has the following characteristics:

Initial mass = 200kgMass after rocket operation = 130 kg

Payload, nonpropulsive structure, etc., = 110 kg

Rocket operation duration = 3.0 sec

Average specific impulse of propellant = 240 sec

Determine the vehicles (i) mass ratio, (ii) propellant mass fraction, (iii) propellant flow rate, (iv)

thrust, (v) thrust-to-weight ratio, (vi) acceleration of the vehicle, (vii) effective exhaust velocity,

(viii) total impulse, and (ix) the impulse to weight ratio.

Solution:

(i) Mass ratio of vehicle, mf/mp = 130/200 = 0.65Mass ratio of rocket system = mf/mo = (130-110)/(200-110) = 20/90 = 0.222

(ii)Propellant mass fraction = (mo mf)/mo = (90-20)/90 = 0.778(iii)Propellant mass flow rate = 70/3 = 23.3 kg/sec

(iv)Thrust = osp gmI = 240 x 23.3 x 9.81 = 54.857 N(v)

Thrust-to-weight ratio of the vehicle is

Initial value = 54,857 / (200 x 9.81) = 28

Final value = 54,857 / (130 x 9.81) = 43

(vi) Maximum acceleration of the vehicle is 43 x 9.81 = 421 m/sec2(vii) The effective exhaust velocity is

c = Isp go = 240 x 9.81 = 2354 m/sec

(viii) Total impulse = Isp w = 240 x 70 x 9.81 = 164, 808 N-secThis result can also be obtained by multiplying the thrust by the duration.

(ix)The impulse to weight ratio of the propulsion system is= 164,808 / [(200-110) x 9.81] = 187

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Q2. The following measurements were made in a sea level test of a solid propellant rocket

motor:

Burn duration = 40 sec

Initial mass before test = 1210 kg

Mass of rocket motor after test = 215 kg

Average thrust = 62,250 N

Chamber pressure = 7.00 MPa

Nozzle exit pressure = 0.070 MPa

Nozzle throat diameter = 0.855 m

Nozzle exit diameter = 0.2703 m

Determine spIandccvm ,,, 2

at sea level, and c and Isp at 1000 and 25,000 m altitude.

Assume an invariant thrust and mass flow rate and negligible short start and stop

transients.

Solution:

Mass flow rate = (initial motor mass final motor mass)/burn time

= (1210 215) / 40 = 24.9 kg/sec

The nozzle areas at the throat and exit are

At = D2 /4 = x 0.0855

2 /4 = 0.00574 m2

A2 = D2 /4 = x 0.2703

2 /4 = 0.0574 m

2

The actual exhaust velocity

=m

AppFv

))((2322

= (62,250 (0.070-0.1013) 106x 0.0574) / 24.9

= 2572 m/sec

=

m

ApC t1

= 7.00 x 106x 0.00574/24.9 = 1613 m/sec

Isp = 62,250 / (24.9 x 9.81) = 255 sec

c = 255 x 9.81 = 2500 m/sec

For altitudes of 1000 and 25, 000 m the ambient pressure (see atmospheric table) is 0.898 and

0.00255 MPa.

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+=

m

Appvc 2322

)(

At 1000 m altitude,

c = 2572 + (0.070-0.898) x 106 x 0.0574/24.9 = 2527 m/sec

Isp = 2527/9.81 = 258 sec

At 25,000 m altitude,

c = 2572 + (0.070-0.00255) x 106x 0.0574/24.9 = 2727 m/sec

Isp = 2727/9.81 = 278 sec

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Rocket Nozzles

Purpose:

The nozzle is the component of a rocket or air-breathing engine that produces thrust. This isaccomplished by converting the thermal energy of the hot chamber gases into kinetic energy and

directing that energy along the nozzle's axis, as illustrated below.

Simple representation of a rocket nozzle

Although simplified, this figure illustrates how a rocket nozzle works. The propellant iscomposed of a fuel, typically liquid hydrogen (H 2), and an oxidizer, typically liquid oxygen (O

2). The propellant is pumped into a combustion chamber at some rate (mdot) where the fueland oxidizer are mixed and burned. The exhaust gases from this process are pushed into the

throat region of the nozzle. Since the throat is of less cross-sectional area than the rest of the

engine, the gases are compressed to a high pressure. The nozzle itself gradually increases incross-sectional area allowing the gases to expand. As the gases do so, they push against the walls

of the nozzle creating thrust.

Mathematically, the ultimate purpose of the nozzle is to expand the gases as efficiently as

possible so as to maximize the exit velocity (v exit). This process will maximize the thrust (F)

produced by the system since the two are directly related by the equation

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where

F = thrust force

= mass flow rate

v exit = exhaust gas velocity at the nozzle exit

p exit = pressure of the exhaust gases at the nozzle exit

p = ambient pressure of the atmosphere

A exit = cross-sectional area of the nozzle exit

Expansion Area Ratio:

In theory, the only important parameter in rocket nozzle design is the expansion area ratio ( ), or

the ratio of exit area (A exit) to throat area (A throat).

Fixing all other variables (primarily the chamber pressure), there exists only one such ratio thatoptimizes overall system performance for a given altitude (or ambient pressure). However, arocket typically does not travel at only one altitude. Thus, an engineer must be aware of the

trajectory over which a rocket is to travel so that an expansion ratio that maximizes performance

over a range of ambient pressures can be selected.

Nevertheless, other factors must also be considered that tend to alter the design from this

expansion ratio-based optimum. Some of the issues designers must deal with are nozzle weight,length, manufacturability, cooling (heat transfer), and aerodynamic characteristics.

Typical temperatures (T) and pressures (p) and speeds (v) in a De Laval Nozzle

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Maximum thrust for a rocket engine is achieved by maximizing the momentum contribution of

the equation without incurring penalties from over expanding the exhaust. This occurs when Pe =

Pamb. Since ambient pressure changes with altitude, most rocket engines spend very little time

operating at peak efficiency.

If the pressure of the exhaust jet varies from atmospheric pressure, nozzles can be said to beunderexpanded, ambient or overexpanded. If under or overexpanded then loss of efficiency

occurs, grossly overexpanded nozzles lose less efficiency, but the exhaust jet is usually unstable.

Rockets become progressively more underexpanded as they gain altitude. Note that almost allrocket engines will be momentarily grossly overexpanded during startup in an atmosphere.

Rocket Nozzle Shapes

Not all rocket nozzles are alike, and the shape selected usually depends on the application.

This section discusses the basic characteristics of the major classes of nozzles used today.

Nozzle Comparisons:

To date three major types of nozzles, the cone, the bell or contoured, and the annular or plug,have been employed. Each class satisfies the design criteria to varying degrees. Examples of

these nozzle types can be seen below.

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Size comparison of optimal cone, bell, and radial nozzles for a given set

of conditions

Conical Nozzle:

The conical nozzle was used often in early rocket applications because of its simplicity andease of construction. The cone gets its name from the fact that the walls diverge at a constant

angle. A small angle produces greater thrust, because it maximizes the axial component ofexit velocity and produces a high specific impulse (a measure of rocket efficiency). Thepenalty, however, is a longer and heavier nozzle that is more complex to build. At the other

extreme, size and weight are minimized by a large nozzle wall angle. Unfortunately, large

angles reduce performance at low altitude because the high ambient pressure causesoverexpansion and flow separation.

Bell Nozzle:

The bell, the most commonly used nozzle shape, offers significant advantages over theconical nozzle, both in size and performance. Referring to the above figure, note that the bell

consists of two sections. Near the throat, the nozzle diverges at a relatively large angle but thedegree of diveregence tapers off further downstream. Near the nozzle exit, the diveregenceangle is very small. In this way, the bell is a compromise between the two extremes of the

conical nozzle since it minimizes weight while maximizing performance. The most important

design issue is to contour the nozzle to avoid oblique shocks and maximize performance.

However, we must remember that the final bell shape will only be the optimum at oneparticular altitude.

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Annular Nozzles:

The annular nozzle, also sometimes known as the plug or "altitude-compensating" nozzle, isthe least employed of those discussed due to its greater complexity. The term "annular" refers

to the fact that combustion occurs along a ring, or annulus, around the base of the nozzle.

"Plug" refers to the centerbody that blocks the flow from what would be the center portion ofa traditional nozzle. "Altitude-compensating" is sometimes used to describe these nozzles

since that is their primary advantage, a quality that will be further explored later.

Before describing the various forms of annular nozzles, it is useful to mention some key

differences in design parameters from the conical or bell nozzles. The expansion area ratio

for a traditional nozzle has already been discussed. When considering an annular nozzle, thearea of the centerbody (A plug) must also be taken into account.

Another parameter particular to this type of nozzle is the annular diameter ratio, D p / D t, orthe ratio of the centerbody diameter to that of the throat. The ratio is used as a measure of the

nozzle geometry for comparison with other plug nozzle shapes. Typical values of this ratioappear in the above figure.

Annular Nozzles I

Having introduced the three principal families of nozzle shapes, we will now look more closely

at the two major subclasses of annular, or plug, nozzles.

Radial Out-Flow Nozzles:

Two major types of plug nozzles have been developed to date. They are distinguished by themethod in which they expand the exhaust, outward or inward. The radial out-flow nozzle was the

subject of much research in the late 1960s and early 1970s. Examples of this type are theexpansion-deflection (E-D), reverse-flow (R-F), and horizontal-flow (H-F) nozzles shown in the

figure above.

The name of each of these nozzles indicates how it functions. The expansion-deflection nozzle

works much like a bell nozzle since the exhaust gases are forced into a converging throat region

of low area before expanding in a bell-shaped nozzle. However, the flow is deflected by a plug,or centerbody, that forces the gases away from the center of the nozzle. Thus, the E-D is a radial

out-flow nozzle.

The reverse-flow nozzle gets its name because the fuel is injected from underneath, but the

exhaust gases are rotated 180 thereby reversing their direction. Similarly, the fuel in the

horizontal-flow nozzle is injected sideways, but the exhaust is rotated 90.

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Judging by the amount of literature obtained on this subject, little work has been done on the R-F

and H-F nozzles, and they will not be considered further. The E-D, on the other hand, has beenone of the most studied forms of annular nozzles. While similar in nature to the bell nozzle, the

most notable difference is the addition of a centerbody. As shown below, this "plug" may be

located upstream of, downstream of, or in the throat, with each location resulting in better

performance for a given set of operating conditions.

Comparison of centerbody locations in Expansion-Deflection

nozzles [from Conley et al, 1984]

The purpose of the centerbody is to force the flow to remain attached to, or to stick to, the nozzle

walls, as illustrated in the following figure.

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Expansion-deflection nozzle flow behavior at low altitude

[from Sutton, 1992]

This behavior is desirable at low altitudes because the atmospheric pressure is high and may begreater than the pressure of the exhaust gases. When this occurs, the exhaust is forced inward and

no longer exerts force on the nozzle walls, so thrust is decreased and the rocket becomes less

efficient. The centerbody, however, increases the pressure of the exhaust gases by squeezing thegases into a smaller area thereby virtually eliminating any loss in thrust at low altitude.

Annular Nozzles II

Having introduced the three principal families of nozzle shapes and discussed the radial out-flow

nozzle, we will now look more closely at the second class of annular nozzles.

Radial In-Flow Nozzles:

The second major variety of annular nozzles is the radial in-flow type, exemplified by the spike

shown above.

This type of nozzle, named for the prominent spike centerbody, is often described as a bell

turned inside out. However, the nozzle shown above is only one of many possible spike

configurations. Variations of this design, shown below, include

(a) a traditional curved spike with completely external supersonic expansion

(b) a similar shape in which part of the expansion occurs internally

(c) a design similar to the expansion-deflection nozzle in which all expansion occurs

internally.

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Example of a truncated, conical spike [from Berman and Crimp, 1961]

As any fluid dynamicist recognizes, the significant disadvantage of the "flat" plug is that aturbulent wake forms aft of the base at high altitudes resulting in high base drag and reduced

efficiency. However, this problem can be greatly alleviated in an improved version of the

truncated spike that introduces a "base bleed," or secondary subsonic flow, into the region aft ofthe base.

Example of an aerospike nozzle with a subsonic, recirculating flow

[from Hill and Peterson, 1992]

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Aerospike Flowfield:

The exact nature of the exhaust flowfield behind an aerospike nozzle is currently the subject of

much research. The most notable features of a typical aerospike nozzle flowfield are shown inmore detail below.

Flowfield characteristics of an aerospike nozzle [from Ruf and McConnaughey, 1997]

The primary exhaust can be seen expanding against the centerbody and then around the corner of

the base region. The interaction of this flow with the re-circulating base bleed creates an inner

shear layer. The outer boundary of the exhaust plume is free to expand to ambient pressure.Expansion waves can be seen emanating from the thruster exit lip, and these waves reflect from

the centerbody contour to the free jet boundary. Compression waves are then reflected back and

may merge to form the envelope shock seen in the primary exhaust.

At low altitude (high ambient pressure), the free boundary remains close to the nozzle (see

below) causing the compression waves to reflect onto the centerbody and shear layer themselves.The waves impacting the centerbody increase pressure on the surface, thereby increasing the

centerbody component of thrust. The waves impacting the shear layer, on the other hand,

increase the circulation of the base flow thereby increasing the base component of thrust.

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Aerospike nozzle behavior during flight [from Rocketdyne, 1999]

Thrust vectoring: Because the combustion chambers can be controlled individually, thevehicle can be maneuvered using differential thrust vectoring. This eliminates the need

for the heavy gimbals and actuators used to vary the direction of traditional nozzles.

Aerospike thrust vectoring control [from Rocketdyne, 1999]

Additional Reading

1. Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons Inc., New York, 7 thEdn., 2001.